754 THE PRINCIPLES OF SCIENCE. [CHAP. 



The science of crystallography is that perhaps in which 

 the most precise and general laws have been detected, but 

 it would be untrue to assert that it has lessened the area of 

 future discovery. "We can show that each one of the seven 

 or eight hundred forms of calcite is derivable by geome- 

 trical modifications from an hexagonal prism ; but who has 

 attempted to explain the molecular forces producing these 

 modifications, or the chemical conditions in which they arise ? 

 The law of isomorphism is an important generalisation, for 

 it establishes a general resemblance between the forms of 

 crystallisation of natural classes of elements. But if we 

 examine a little more closely we find that these forms are 

 only approximately alike, and the divergence peculiar to 

 each substance is an unexplained exception. 



By many similar illustrations it might readily be shown 

 that in whatever direction we extend our investigations 

 and successfully harmonise a few facts, the result is only 

 to raise up a host of other unexplained facts. Can any 

 scientific man venture to state that there is less opening 

 now for new discoveries than there was three centuries ago ? 

 Is it not rather true that we have but to open a scientific 

 book and read a page or two, and we shall come to some 

 recorded phenomenon of which no explanation can yet 

 be given ? In every such fact there is a possible opening 

 for new discoveries, and it can only be the fault of the 

 investigator's mind if he can look around him and find 

 no scope for the exercise of his faculties. 



Infinite Incompleteness of the Mathematical Sciences. 



There is one privilege which a certain amount of know- 

 ledge should confer ; it is that of becoming aware of the 

 weakness of our powers compared with the tasks which 

 they might undertake if stronger. To the pooi savage who 

 cannot count twenty the arithmetical accomplishments of 

 the schoolboy are miraculously great. The schoolboy cannot 

 comprehend the vastly greater powers of the student, who 

 has acquired facility in algebraic processes. The student 

 can but look with feelings of surprise and reverence at the 

 powers of a Newton or a Laplace. But the question at 

 once suggests itself, Do the powers of the highest human 

 intellect bear a finite ratio to the things which are to be 



